This invention relates generally to reconstruction of computed tomographic (CT) images, and more particularly to generation of thick image slices utilizing 3D backprojection.
In some known CT imaging system configurations, an x-ray source projects a fan-shaped beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system and generally referred to as an “imaging plane”. The x-ray beam passes through an object being imaged, such as a patient. The beam, after being attenuated by the object, impinges upon an array of radiation detectors. The intensity of the attenuated radiation beam received at the detector array is dependent upon the attenuation of an x-ray beam by the object. Each detector element of the array produces a separate electrical signal that is a measurement of the beam intensity at the detector location. The intensity measurements from all the detectors are acquired separately to produce a transmission profile.
In third generation CT systems, the x-ray source and the detector array are rotated with a gantry within the imaging plane and around the object to be imaged such that the angle at which the x-ray beam intersects the object constantly changes. A group of x-ray attenuation measurements, i.e., projection data, from the detector array at one gantry angle is referred to as a “view”. A “scan” of the object comprises a set of views made at different gantry angles, or view angles, during one revolution of the x-ray source and detector.
In an axial scan, the projection data is processed to construct an image that corresponds to a two-dimensional slice taken through the object. One method for reconstructing an image from a set of projection data is referred to in the art as the filtered backprojection technique. This process converts the attenuation measurements from a scan into integers called “CT numbers” or “Hounsfield units” (HU), which are used to control the brightness of a corresponding pixel on a cathode ray tube display.
To reduce the total scan time, a “helical” scan may be performed. To perform a “helical” scan, the patient is moved while the data for the prescribed number of slices is acquired. Such a system generates a single helix from a fan beam helical scan. The helix mapped out by the fan beam yields projection data from which images in each prescribed slice may be reconstructed.
Reconstruction algorithms for helical scanning typically use helical weighing algorithms that weight the collected data as a function of view angle and detector channel index. Specifically, prior to a filtered backprojection process, the data is weighted according to a helical weighing factor, which is a function of both the gantry angle and detector angle. The weighted data is then processed to generate CT numbers and to construct an image that corresponds to a two-dimensional slice taken through the object.
To further reduce the total acquisition time, multi-slice CT has been introduced. In multi-slice CT, multiple rows of projection data are acquired simultaneously at any time instant. When combined with helical scan mode, the system generates a single helix of cone beam projection data. Similar to the single slice helical, weighting scheme, a method can be derived to multiply the weight with the projection data prior to the filtered backprojection algorithm.
For moderate cone beam angles, artifacts produced by FDK-type reconstructions are adequately suppressed. With the increased volume coverage enabled by known multi-slice CT detectors, however, cone beam related image artifacts can no longer be ignored. Because of the 3D-backprojection process used in FDK-type reconstructions, the z-filtering technique used in 2D approximations does not necessarily provide adequate results. To fully understand the issue, a 2D z-filtering technique used in at least one known CT imaging apparatus is described.
Let us denote by w′(γ, β, n) the weighting function for a projection sample at detector channel γ, view angle β, and detector row n. The weighted projection, p′(γ, β, n), is then written:p′(γ,β,n)=w′(γ,β,n)p(γ,β,n).  (1)
In equation (1), the weighting function can be obtained by convolving the weighting function in the “native mode” (in which no slice broadening is intended), w(γ, β, n), with a z-filter function, ƒ(β) (because β is linearly related to z):w′(γ,β,n)=w(γ,β,n){circle around (×)}ƒ(β)  (2)
Because the cone angle is ignored, the multiple detector rows and view angles are summed to produce a single 2D sinogram, s(γ, β):
                              s          ⁡                      (                          γ              ,              β                        )                          =                              ∑                                          ∀                                  β                  ′                                            =                              β                ±                                  2                  ⁢                  π                                                                                                    ⁢                                          ⁢                                    ∑                              n                =                1                            N                        ⁢                                                  ⁢                                                            p                  ′                                ⁡                                  (                                      γ                    ,                    β                    ,                    n                                    )                                            .                                                          (        3        )            
For any reconstruction method that employs 3D backprojection (such as FDK-type reconstructions), the difference between the samples collected from different detector rows cannot be ignored, since the row location becomes reconstruction pixel dependent. Consequently, this formulation is no longer valid and the resulting artifacts can be significant.
More particularly, in at least one known method of reconstruction and referring to FIG. 8, for a given source trajectory 80, x-rays will pass from a moving source 14 through an object (not shown) and onto a multirow detector array 18. A weighted and filtered backprojection is back-projected in 3D so that each backprojection path 802 corresponds to an x-ray path (i.e., pixel-driven backprojection rays) that generated the projection sample. Because each detector element (individual detector elements are not shown in FIG. 6) has a finite size (and also a finite width and height), rays 802 cast from each pixel will not, in general, always land on a center of a detector row 804. For this reason, at least one known 3D backprojection method uses linear interpolation between measured samples to arrive at an interpolated sample for reconstruction.
Some of the samples used in this reconstruction are obtained by contributions from two detector rows and some are obtained with a single detector row. The relative contribution from the two rows also depends on the relative row location with respect to the intersection point. In helical mode, the interpolation occurs in a periodic fashion and leads to a periodic artifact pattern when the scanned object changes quickly in z, as shown in the prior art reconstruction of FIG. 9.